U.S. patent application number 16/730331 was filed with the patent office on 2021-07-01 for grad neural networks for unstructured data.
The applicant listed for this patent is International Business Machines Corporation. Invention is credited to Elliot Holtham, Lior Horesh, Raya Horesh.
Application Number | 20210201109 16/730331 |
Document ID | / |
Family ID | 1000004592717 |
Filed Date | 2021-07-01 |
United States Patent
Application |
20210201109 |
Kind Code |
A1 |
Horesh; Lior ; et
al. |
July 1, 2021 |
GRAD NEURAL NETWORKS FOR UNSTRUCTURED DATA
Abstract
An illustrative embodiment includes a method for analyzing
unstructured multidimensional data with a neural network. The
method includes designing the neural network at least in part by
defining differential operators conforming with dimensions of the
data. The method also includes performing forward propagation at a
given convolution layer of the neural network at least in part by:
obtaining one or more convolved values at least in part by
performing convolution over an object within the data, processing
respective convolved values to obtain output, and updating the
object based at least in part on the output.
Inventors: |
Horesh; Lior; (North Salem,
NY) ; Horesh; Raya; (North Salem, NY) ;
Holtham; Elliot; (Vancouver, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
International Business Machines Corporation |
Armonk |
NY |
US |
|
|
Family ID: |
1000004592717 |
Appl. No.: |
16/730331 |
Filed: |
December 30, 2019 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06F 16/322 20190101;
G06N 3/04 20130101 |
International
Class: |
G06N 3/04 20060101
G06N003/04; G06F 16/31 20060101 G06F016/31 |
Claims
1. A method for analyzing unstructured multidimensional data with a
neural network, the method comprising: designing the neural network
at least in part by defining differential operators conforming with
dimensions of the data; and performing forward propagation at a
given convolution layer of the neural network at least in part by:
obtaining one or more convolved values at least in part by
performing convolution over an object within the data; processing
respective convolved values to obtain output; and updating the
object based at least in part on the output.
2. The method of claim 1, wherein processing the respective
convolved values comprises performing non-linear activation of the
respective convolved values.
3. The method of claim 1, wherein processing the respective
convolved values comprises normalizing the respective convolved
values.
4. The method of claim 1, wherein: the defined differential
operators comprise divergence, gradient and curl; obtaining a given
one of the convolved values comprises performing pointwise
convolution of a respective gradient computed for a corresponding
one of the dimensions of the object; and the output comprises a
divergence computed from the processed convolved gradients.
5. The method of claim 4, wherein processing the respective
convolved values comprises applying tensor contraction of the
corresponding dimension to the given one of the convolved
values.
6. The method of claim 1, wherein at least a portion of the
multidimensional data is irregularly sampled, and wherein analyzing
the data comprises at least one of prediction and classification by
the neural network without resampling the irregularly sampled
data.
7. The method of claim 1, wherein responsive to the
multidimensional data comprising more than two dimensions, defining
the one or more differential operators comprises defining one or
more tensorial differential operators.
8. The method of claim 7, wherein further responsive to the
multidimensional data comprising more than two dimensions,
processing the respective convolved values to obtain the output
comprises applying tensor contraction to the respective convolved
values.
9. The method of claim 1, wherein obtaining one or more convolved
values comprises: when dimensions of the given layer match
dimensions of at least another layer of the neural network,
performing pointwise convolution over the object; and when
dimensions of the given layer do not match dimensions of another
layer of the neural network, performing grouped convolution over
the object.
10. The method of claim 1, wherein the neural network is designed
based at least in part on a partial differential equations
architecture, and wherein the architecture is at least one of
elliptic, parabolic and hyperbolic.
11. The method of claim 1, wherein the differential operators are
defined on a tree structure.
12. The method of claim 1, wherein designing the neural network
further comprises defining a time stepping, and wherein the object
is updated based at least in part on the output and on the time
stepping.
13. The method of claim 12, wherein the neural network is designed
based at least in part on a hyperbolic architecture, and wherein
the time stepping is defined using at least a second order
derivative.
14. The method of claim 1, wherein designing the neural network
further comprises defining one or more averaging mappings
conforming with the dimensions of the data.
15. The method of claim 14, wherein the one or more averaging
mappings conforming with the dimensions of the data comprise at
least one of a cell to edge mapping and a face to node mapping.
16. The method of claim 1, wherein designing the neural network
further comprises defining at least one of a loss function and an
accuracy measure.
17. The method of claim 1, wherein designing the neural network
further comprises defining at least one of network architecture and
network geometry.
18. The method of claim 1, wherein designing the neural network
further comprises defining at least one of spatial discretization
and temporal discretization.
19. An apparatus for analyzing unstructured multidimensional data
with a neural network, the method comprising: a memory; and at
least one processor coupled to the memory, the processor being
operative: to design the neural network at least in part by
defining differential operators conforming with dimensions of the
data; and to perform forward propagation at a given convolution
layer of the neural network at least in part by: obtaining one or
more convolved values at least in part by performing convolution
over an object within the data; processing respective convolved
values to obtain output; and updating the object based at least in
part on the output.
20. A computer program product comprising a non-transitory
machine-readable storage medium having machine-readable program
code embodied therewith, said machine-readable program code
comprising machine-readable program code configured: to design a
neural network at least in part by defining differential operators
conforming with dimensions of a set of unstructured
multidimensional data; and to perform forward propagation at a
given convolution layer of the neural network at least in part by:
obtaining one or more convolved values at least in part by
performing convolution over an object within the set of data;
processing respective convolved values to obtain output; and
updating the object based at least in part on the output.
Description
NAMES OF PARTIES TO JOINT RESEARCH AGREEMENT
[0001] The present invention was made as a result of activities
undertaken within the scope of a joint research agreement between
International Business Machines Corporation (IBM) and Xtract
Technologies, Inc. that was in effect on or before the effective
filing date of the invention.
BACKGROUND
[0002] The present invention relates to the electrical, electronic
and computer arts, and, more particularly, to computational
approaches for artificial intelligence (AI) applications.
[0003] Convolutional neural network (CNN) architectures have
revolutionized the field of AI for segmentation, detection and
classification tasks. Convolution computation often accounts for
the majority of computational costs, particularly during inference
during deployment. Spatial correlations are frequently local, and
therefore architecture that is inspired by the notion of locality,
harnessing primitives of physical processes (in the form of local
differential operators), can be advantageous and much more
computationally efficient.
[0004] Traditionally, convolutions must be applied on uniform
grids: convolution operations operate via dimensioned stencils
(3.times.3, 5.times.5, 7.times.7 etc.) on a regular pixelated grid
either in one, two or three dimensions. However, many datasets do
not come on regularly sampled grids. For example, point cloud data
from sensors such as LIDAR (Light Detection and Ranging) on
driverless cars and/or drones is often arranged as an irregular set
of 3D (three-dimensional) points. Likewise, geospatial and/or
geophysical data is often recorded on irregular grids. More
generally, images and videos can often be represented more
efficiently on irregular grids than on uniform grids. Thus, there
is a long-felt and unmet need for predictions and classifications
which could be applied directly to such data without
re-gridding.
SUMMARY
[0005] An illustrative embodiment includes a method for analyzing
unstructured multidimensional data with a neural network. The
method includes designing the neural network at least in part by
defining differential operators conforming with dimensions of the
data. The method also includes performing forward propagation at a
given convolution layer of the neural network at least in part by:
obtaining one or more convolved values at least in part by
performing convolution over an object within the data, processing
respective convolved values to obtain output, and updating the
object based at least in part on the output.
[0006] As used herein, "facilitating" an action includes performing
the action, making the action easier, helping to carry the action
out, or causing the action to be performed. Thus, by way of example
and not limitation, instructions executing on one processor might
facilitate an action carried out by instructions executing on a
remote processor, by sending appropriate data or commands to cause
or aid the action to be performed. For the avoidance of doubt,
where an actor facilitates an action by other than performing the
action, the action is nevertheless performed by some entity or
combination of entities.
[0007] One or more embodiments of the invention or elements thereof
can be implemented in the form of a computer program product
including a computer readable storage medium with computer usable
program code for performing the method steps indicated.
Furthermore, one or more embodiments of the invention or elements
thereof can be implemented in the form of a system (or apparatus)
including a memory, and at least one processor that is coupled to
the memory and operative to perform exemplary method steps. Yet
further, in another aspect, one or more embodiments of the
invention or elements thereof can be implemented in the form of
means for carrying out one or more of the method steps described
herein; the means can include (i) hardware module(s), (ii) software
module(s) stored in a computer readable storage medium (or multiple
such media) and implemented on a hardware processor, or (iii) a
combination of (i) and (ii); any of (i)-(iii) implement the
specific techniques set forth herein.
[0008] Illustrative embodiments of the present invention have
practical applications and provide technological improvements.
Illustrative embodiments enable deep neural networks to be applied
to multidimensional (e.g., 3D) data volumes with substantial
computational cost reduction compared to state-of-the-art
algorithms. Illustrative embodiments advantageously provide an
efficient and robust neural network design that harnesses
differential operators and averaging maps for irregularly sampled
data. For example, illustrative embodiments harness a partial
differential equation (PDE) inspired framework, based upon standard
convolutional neural network concepts, to handle sparse input data
effectively. Thus, illustrative embodiments provide predictions and
classifications without requiring data resampling and interpolation
which wastes computational resources and creates undesirable
artifacts. Illustrative embodiments allow differential operations
to be applied to more general data representations than
conventional techniques where convolutions must be applied on
uniform grids. By way of example, illustrative embodiments may
define differential operators on unstructured (e.g. tetrahedral)
grids, thereby allowing differential operator formulations to be
applied to graph and tree structures (e.g., quadtree) with
connected relationships, which are common in networking
applications.
[0009] These and other features and advantages of the present
invention will become apparent from the following detailed
description of illustrative embodiments thereof, which is to be
read in connection with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 is a simplified flowchart showing an exemplary
technique for designing a neural network in accordance with an
aspect of the invention;
[0011] FIG. 2 is a simplified flowchart showing an exemplary
technique for forward propagation in accordance with an aspect of
the invention; and
[0012] FIG. 3 shows a computer system that may be useful in
implementing one or more aspects and/or elements of the
invention.
DETAILED DESCRIPTION
[0013] FIG. 1 is a simplified flowchart showing an exemplary
technique 100 for designing a neural network in accordance with an
aspect of the invention. As previously discussed, illustrative
embodiments advantageously provide an efficient and robust neural
network design that harnesses differential operators and averaging
maps for irregularly sampled data. For example, illustrative
embodiments harness a partial differential equation inspired
framework, based upon standard convolutional neural network
concepts, to handle sparse input data effectively. In step 110,
training and testing data may be loaded from a data set.
[0014] In step 120, differential operators (e.g., divergence,
gradient, curl, etc.) as well as averaging mappings (e.g., cell to
edge, face to node, etc.) are defined over the domain of the
problem (e.g., indicated by the dataset). For a data set of
two-dimensional (2D) images, these will be 2D differential
operators conforming with the dimensions of the images. For
higher-dimensional data, tensorial differential operators will be
defined.
[0015] In step 130, the loss function (e.g., cross entropy) and
accuracy measures are defined. In step 140, the network
architecture is defined. The network architecture defined in step
140 may include, for example, residual network (ResNet), long
short-term memory (LSTM), and/or gated recurrent unit (GRU). In
step 150, the network geometry, spatial and temporal discretization
are defined. Step 150 may include defining h and dt, where h is an
encoder output, and dt is the decoder hidden state at time step t,
which captures the previous output sequence context.
[0016] FIG. 2 is a simplified flowchart showing an exemplary
technique 200 for forward propagation in accordance with an aspect
of the invention. Technique 200 may be repeated for respective
convolution layers within a neural network. Step 210 determines
whether the layers are of matching dimensions. If step 210
determines the layers are of matching dimensions, then technique
200 proceeds to steps 220 through 260.
[0017] Step 220 computes network gradients (e.g., Ix, Iy) of
respective dimensions of the object I. Step 230 applies tensor
contraction (e.g., 1.times.1 convolution) of the appropriate
dimension to the gradients. Thus, step 230 includes computing
zx=conv1.times.1T (conv1.times.1(Ix)) and zy=conv1.times.1T
(conv1.times.1(Iy)), where conv1.times.1 denotes a 1.times.1
(pointwise) convolution, and conv1.times.1T denotes a tensor
contraction.
[0018] Step 240 performs normalization (instanceNorm) upon each
convolved input (zx, zy) followed by non-linear activation
function, such as a rectified linear unit (ReLU). Thus, step 240
may include computing zx=Relu(instanceNorm(zx)) and
zy=Relu(instanceNorm(zy)). Step 250 involves computing divergence,
e.g., z=divergence(zx,zy). Step 260 updates the object I based on
the dt from step 150 and the divergence z from step 250, e.g.,
I=I+dt*z.
[0019] If step 210 determines that the layers do not have matching
dimensions, then technique 200 proceeds to steps 280 and 290. Step
280 forms a grouped N.times.N convolutional layer (e.g., 3.times.3,
5.times.5, 7.times.7 etc.). Thus, step 280 may include computing
grouped 3.times.3 convolution over the object I, e.g.,
z=conv3.times.3(I). Step 290 performs normalization (instanceNorm)
upon each convolved input (zx, zy) followed by non-linear
activation function, and then updates the object I. For example,
step 290 may include computing I=Relu(instanceNorm(z)).
[0020] An illustrative embodiment of the present invention has
demonstrated unexpected results. As previously discussed,
conventional convolutions must be applied on uniform grids, but
images can often be represented more efficiently on irregular
grids. An illustrative embodiment of the present invention
advantageously allows for classifications to be applied directly to
such data without re-gridding, while conventional techniques
require data resampling and interpolation which wastes
computational resources and creates undesirable artifacts. Thus, an
illustrative embodiment of the present invention enables deep
neural networks to be applied to image data with substantial
computational cost reduction compared to state-of-the-art
algorithms.
[0021] The CIFAR10 dataset includes a total of 60,000 color images,
each having a size of 32 pixels by 32 pixels. There are 6000 images
in each of 10 different classes: airplanes, cars, birds, cats,
deer, dogs, frogs, horses, ships, and trucks. The inventors used a
basic architecture according to an illustrative embodiment of the
present invention to perform image classification of the CIFAR10
dataset with over 90% accuracy.
[0022] Although the illustrative embodiments described herein
primarily utilize elliptic PDE, one skilled in the art will
appreciate that other differential equation architectures (e.g.,
parabolic or hyperbolic) may be utilized with embodiments of the
present invention. For example, in an illustrative embodiment with
a hyperbolic architecture, the time stepping dt discussed above
with reference to steps 150 and 250 may involve a second
derivative.
[0023] One or more embodiments of the invention, or elements
thereof, can be implemented, at least in part, in the form of an
apparatus including a memory and at least one processor that is
coupled to the memory and operative to perform exemplary method
steps.
[0024] One or more embodiments can make use of software running on
a general purpose computer or workstation. With reference to FIG.
3, such an implementation might employ, for example, a processor
902, a memory 904, and an input/output interface formed, for
example, by a display 906 and a keyboard 908. The term "processor"
as used herein is intended to include any processing device, such
as, for example, one that includes a CPU (central processing unit)
and/or other forms of processing circuitry. Further, the term
"processor" may refer to more than one individual processor. The
term "memory" is intended to include memory associated with a
processor or CPU, such as, for example, RAM (random access memory),
ROM (read only memory), a fixed memory device (for example, hard
drive), a removable memory device (for example, diskette), a flash
memory and the like. In addition, the phrase "input/output
interface" as used herein, is intended to include, for example, one
or more mechanisms for inputting data to the processing unit (for
example, mouse), and one or more mechanisms for providing results
associated with the processing unit (for example, printer). The
processor 902, memory 904, and input/output interface such as
display 906 and keyboard 908 can be interconnected, for example,
via bus 910 as part of a data processing unit 912. Suitable
interconnections, for example via bus 910, can also be provided to
a network interface 914, such as a network card, which can be
provided to interface with a computer network, and to a media
interface 916, such as a diskette or CD-ROM drive, which can be
provided to interface with media 918.
[0025] Accordingly, computer software including instructions or
code for performing the methodologies of the invention, as
described herein, may be stored in one or more of the associated
memory devices (for example, ROM, fixed or removable memory) and,
when ready to be utilized, loaded in part or in whole (for example,
into RAM) and implemented by a CPU. Such software could include,
but is not limited to, firmware, resident software, microcode, and
the like.
[0026] A data processing system suitable for storing and/or
executing program code will include at least one processor 902
coupled directly or indirectly to memory elements 904 through a
system bus 910. The memory elements can include local memory
employed during actual implementation of the program code, bulk
storage, and cache memories which provide temporary storage of at
least some program code in order to reduce the number of times code
must be retrieved from bulk storage during implementation.
[0027] Input/output or I/O devices (including but not limited to
keyboards 908, displays 906, pointing devices, and the like) can be
coupled to the system either directly (such as via bus 910) or
through intervening I/O controllers (omitted for clarity).
[0028] Network adapters such as network interface 914 may also be
coupled to the system to enable the data processing system to
become coupled to other data processing systems or remote printers
or storage devices through intervening private or public networks.
Modems, cable modem and Ethernet cards are just a few of the
currently available types of network adapters.
[0029] As used herein, including the claims, a "server" includes a
physical data processing system (for example, system 912 as shown
in FIG. 3) running a server program. It will be understood that
such a physical server may or may not include a display and
keyboard.
[0030] It should be noted that any of the methods described herein
can include an additional step of providing a system comprising
distinct software modules embodied on a computer readable storage
medium; the modules can include, for example, any or all of the
elements depicted in the block diagrams or other figures and/or
described herein. The method steps can then be carried out using
the distinct software modules and/or sub-modules of the system, as
described above, executing on one or more hardware processors 902.
Further, a computer program product can include a computer-readable
storage medium with code adapted to be implemented to carry out one
or more method steps described herein, including the provision of
the system with the distinct software modules.
Exemplary System and Article of Manufacture Details
[0031] The present invention may be a system, a method, and/or a
computer program product. The computer program product may include
a computer readable storage medium (or media) having computer
readable program instructions thereon for causing a processor to
carry out aspects of the present invention.
[0032] The computer readable storage medium can be a tangible
device that can retain and store instructions for use by an
instruction execution device. The computer readable storage medium
may be, for example, but is not limited to, an electronic storage
device, a magnetic storage device, an optical storage device, an
electromagnetic storage device, a semiconductor storage device, or
any suitable combination of the foregoing. A non-exhaustive list of
more specific examples of the computer readable storage medium
includes the following: a portable computer diskette, a hard disk,
a random access memory (RAM), a read-only memory (ROM), an erasable
programmable read-only memory (EPROM or Flash memory), a static
random access memory (SRAM), a portable compact disc read-only
memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a
floppy disk, a mechanically encoded device such as punch-cards or
raised structures in a groove having instructions recorded thereon,
and any suitable combination of the foregoing. A computer readable
storage medium, as used herein, is not to be construed as being
transitory signals per se, such as radio waves or other freely
propagating electromagnetic waves, electromagnetic waves
propagating through a waveguide or other transmission media (e.g.,
light pulses passing through a fiber-optic cable), or electrical
signals transmitted through a wire.
[0033] Computer readable program instructions described herein can
be downloaded to respective computing/processing devices from a
computer readable storage medium or to an external computer or
external storage device via a network, for example, the Internet, a
local area network, a wide area network and/or a wireless network.
The network may comprise copper transmission cables, optical
transmission fibers, wireless transmission, routers, firewalls,
switches, gateway computers and/or edge servers. A network adapter
card or network interface in each computing/processing device
receives computer readable program instructions from the network
and forwards the computer readable program instructions for storage
in a computer readable storage medium within the respective
computing/processing device.
[0034] Computer readable program instructions for carrying out
operations of the present invention may be assembler instructions,
instruction-set-architecture (ISA) instructions, machine
instructions, machine dependent instructions, microcode, firmware
instructions, state-setting data, configuration data for integrated
circuitry, or either source code or object code written in any
combination of one or more programming languages, including an
object oriented programming language such as Smalltalk, C++, or the
like, and procedural programming languages, such as the "C"
programming language or similar programming languages. The computer
readable program instructions may execute entirely on the user's
computer, partly on the user's computer, as a stand-alone software
package, partly on the user's computer and partly on a remote
computer or entirely on the remote computer or server. In the
latter scenario, the remote computer may be connected to the user's
computer through any type of network, including a local area
network (LAN) or a wide area network (WAN), or the connection may
be made to an external computer (for example, through the Internet
using an Internet Service Provider). In some embodiments,
electronic circuitry including, for example, programmable logic
circuitry, field-programmable gate arrays (FPGA), or programmable
logic arrays (PLA) may execute the computer readable program
instructions by utilizing state information of the computer
readable program instructions to personalize the electronic
circuitry, in order to perform aspects of the present
invention.
[0035] Aspects of the present invention are described herein with
reference to flowchart illustrations and/or block diagrams of
methods, apparatus (systems), and computer program products
according to embodiments of the invention. It will be understood
that each block of the flowchart illustrations and/or block
diagrams, and combinations of blocks in the flowchart illustrations
and/or block diagrams, can be implemented by computer readable
program instructions.
[0036] These computer readable program instructions may be provided
to a processor of a general purpose computer, special purpose
computer, or other programmable data processing apparatus to
produce a machine, such that the instructions, which execute via
the processor of the computer or other programmable data processing
apparatus, create means for implementing the functions/acts
specified in the flowchart and/or block diagram block or blocks.
These computer readable program instructions may also be stored in
a computer readable storage medium that can direct a computer, a
programmable data processing apparatus, and/or other devices to
function in a particular manner, such that the computer readable
storage medium having instructions stored therein comprises an
article of manufacture including instructions which implement
aspects of the function/act specified in the flowchart and/or block
diagram block or blocks.
[0037] The computer readable program instructions may also be
loaded onto a computer, other programmable data processing
apparatus, or other device to cause a series of operational steps
to be performed on the computer, other programmable apparatus or
other device to produce a computer implemented process, such that
the instructions which execute on the computer, other programmable
apparatus, or other device implement the functions/acts specified
in the flowchart and/or block diagram block or blocks.
[0038] The flowchart and block diagrams in the Figures illustrate
the architecture, functionality, and operation of possible
implementations of systems, methods, and computer program products
according to various embodiments of the present invention. In this
regard, each block in the flowchart or block diagrams may represent
a module, segment, or portion of instructions, which comprises one
or more executable instructions for implementing the specified
logical function(s). In some alternative implementations, the
functions noted in the blocks may occur out of the order noted in
the Figures. For example, two blocks shown in succession may, in
fact, be executed substantially concurrently, or the blocks may
sometimes be executed in the reverse order, depending upon the
functionality involved. It will also be noted that each block of
the block diagrams and/or flowchart illustration, and combinations
of blocks in the block diagrams and/or flowchart illustration, can
be implemented by special purpose hardware-based systems that
perform the specified functions or acts or carry out combinations
of special purpose hardware and computer instructions.
[0039] The descriptions of the various embodiments of the present
invention have been presented for purposes of illustration, but are
not intended to be exhaustive or limited to the embodiments
disclosed. Many modifications and variations will be apparent to
those of ordinary skill in the art without departing from the scope
and spirit of the described embodiments. The terminology used
herein was chosen to best explain the principles of the
embodiments, the practical application or technical improvement
over technologies found in the marketplace, or to enable others of
ordinary skill in the art to understand the embodiments disclosed
herein.
[0040] The terminology used herein is for the purpose of describing
particular embodiments only and is not intended to be limiting of
the invention. As used herein, the singular forms "a", "an" and
"the" are intended to include the plural forms as well, unless the
context clearly indicates otherwise. It will be further understood
that the terms "comprises" and/or "comprising," when used in this
specification, specify the presence of stated features, integers,
steps, operations, elements, and/or components, but do not preclude
the presence or addition of one or more other features, integers,
steps, operations, elements, components, and/or groups thereof.
[0041] The corresponding structures, materials, acts, and
equivalents of all means or step plus function elements in the
claims below are intended to include any structure, material, or
act for performing the function in combination with other claimed
elements as specifically claimed. The description of the present
invention has been presented for purposes of illustration and
description, but is not intended to be exhaustive or limited to the
invention in the form disclosed. Many modifications and variations
will be apparent to those of ordinary skill in the art without
departing from the scope and spirit of the invention. The
embodiment was chosen and described in order to best explain the
principles of the invention and the practical application, and to
enable others of ordinary skill in the art to understand the
invention for various embodiments with various modifications as are
suited to the particular use contemplated.
* * * * *